问题 填空题
向量
a
b
c
满足
a
+
b
+
c
=0,
a
b
,(
a
-
b
)⊥
c
,M=
|a|
|b|
+
|b|
|c|
+
|c|
|a|
,则M=______.
答案

a
+
b
+
c
=0,∴
c
=-(
a
+
b
)

(

a
-
b
)⊥
c
,∴(
a
-
b
)•
c
=0

(

a
-
b
)•[ -(
a
+
b
)]=0,∴|
a
|=|
b
|

∴M=

|
a
|
|
b
|
+
|
b
|
|
c
|
+
|
c
|
|
a
|
+
=1+
|
b
|
|
c
|
+
|
c
|
|
a
|
=1+
|
b
|
|
a
b
|
+
|
a
+
b
|
|
a
|
=1+
2
2
+
2
=1+
3
2
2

故答案为1+

3
2
2

单项选择题 B型题
单项选择题